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algebraic Ancient Egypt arithmetical aroura B. M. Facsimile base Berlin Berlin Papyrus calculation Chapter Four column correct cubic cubits cubit-rods cubit-strips denominator des-jug diameter discussion divided division Document IV Document IV.2 Egyptian mathematics equal equations Example expressed follows formula fragment frustum geometrical Gillings given granary Griffith height hekat Hence henu heqat Hieratic text Hieroglyphic transcription Horus-eye fractions ibid Kahun Kahun Papyrus khar khet length loaves of bread loaves of pefsu measures Moscow Mathematical Papyrus Moscow Papyrus Multiply Neugebauer number of loaves odd numbers palms Papyrus from Chace Peet Peet's Photograph Plate Problem 48 procedure produce pyramid reader Reckon rectangle red auxiliaries Reisner Papyrus remainder result Rhind Mathematical Papyrus Rhind Papyrus scribe seqed setjat solution Struve Take text and Hieroglyphic tion Total translation trapezoid triangle unit fractions unknown quantity Upper-Egyptian grain volume Waerden wedyet-flour
Page 4 - It was this king [Sesotris], moreover, who divided the land into lots and gave everyone a square piece of equal size, from the produce of which he exacted an annual tax. Any man whose holding was damaged by the encroachment of the river would go and declare his loss before the king, who would send inspectors to measure the extent of the loss, in order that he might pay in future a fair proportion of the tax at which his property had been assessed. Perhaps this was the way in which geometry was invented,...
Page 157 - Divide 100 loaves among 5 men in such a way that the shares received shall be in arithmetical progression and that 1/7 of the sum of the largest three shares shall be equal to the sum of the smallest two. What is the difference of the shares?
Page 106 - Das Wesen einer Gleichung besteht nun allerdings weit weniger in dem Wortlaute als in der Auflösung, und so müssen wir, um die Berechtigung unseres Vergleichs zu prüfen, zusehen, wie Ahmes seine Haurechnungen vollzieht.
Page 122 - L'Egypte à l'Exposition universelle de tsûl. (Gazelle des Beauz-Artt, t. XXII et XXIII, Ier et _'' semestres, 1867, in-8*.) Note relative à un papyrus égyptien contenant un fragment d'un traité de géométrie appliquée à l'arpentage.
Page 204 - Mathematischer Papyrus des Staatlichen Museums der Schönen Künste in Moskau.
Page 83 - Take away 1/9 of 9, namely, 1; the remainder is 8. Multiply 8 times 8; it makes 64. Multiply 64 times 10; it makes 640 cubed cubits.
Page 88 - ... are concerned with grain barns. An outstanding accomplishment of the Egyptian mathematics is found however in the entirely correct calculation of the volume of the frustrum of a pyramid with square base, as found in the Moscow papyrus (Plate 5a), by means of the formula where h is the height and a and b the sides of the lower and upper base. It is not to be supposed that such a formula can be found empirically. It must have been obtained on the basis of a theoretical argument; how? By dividing...
Page 58 - ... must now determine whether the progression fulfills the second requirement of the problem: namely, that the number of loaves shall total 100. In other words, multiply the progression whose sum is 60 (see above) by a factor to convert it into 100; the factor, of course, is 1%. This the papyrus does: "As many times as is necessary to multiply 60 to make 100, so many times must these terms be multiplied to make the true series.
Page 26 - ... of five. As being the part which completed the row into one series of the number indicated, the Egyptian r-fraction was necessarily a fraction with, as we should say, unity as the numerator. To the Egyptian mind it would have seemed nonsense and self-contradictory to write...
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